Find the slope of a line, which passes through the origin, and the midpoint of the line-segment joining and points A(0, -4) and B(8, 0).

3

Find the distance between P(x₁, y₁) and Q(x₂, y₂) when (i) PQ is parallel to the y-axis. (ii) PQ is parallel to the x-axis.

4

Find a point on the x-axis, which is equidistant from the points(7, 6) and (3,4).

6

Without using the Pythagoras theorem, show that the points(4, 4), (3,5) and (-1, -1) are the vertices of a right angled triangle.

7

As shown in the figure below, the given line makes an angle of 30⁰ with the positive direction of y-axis in anticlockwise direction.